热浴中的谐振子：精确模拟延时记录数据，精确分析基准统计
Harmonic Oscillator in Heat Bath: Exact simulation of time-lapse-recorded data, exact analytical benchmark statistics
摘要：
用一种对任意大小的时间步长都是精确的算法模拟了热浴中阻尼谐振子的随机动力学。精确的分析结果给出了关联函数和功率谱的形式，他们获得时，从实验时间推移记录计算。讨论了三种应用：（i）有限采样率和采样时间的影响，这里确切地描述，是类似的其他随机动力系统，例如能动的微生物和它们的时间推移记录的轨迹。(ii)任何实验系统都满足相同的统计数据，只要它被解释为有限温度下的阻尼谐振子，例如AFM悬臂梁。(iii)其他三个基本感兴趣的模型是有限温度下阻尼谐振子的极限情况;因此，它弥合了它们的差异，并描述了有限采样率和采样时间对这些模型的影响。最后，我们简要讨论了无量纲化。
英文摘要：
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) Effects of finite sampling-rate and -time, described exactly here, are similar for other stochastic dynamical systems-e.g. motile micro-organisms and their time-lapse recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes effects of finite sampling rate and sampling time for these models as well. Finally, we give a brief discussion of nondimensionalization.
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